I know how precious Bfing is, but at 10 months, my son was exhausting me and I too needed the sleep. He was not sleeping through the night either. I finally decided to try a small bottle of formula (about 4 ounces) after bfing. He finally started sleeping through the night. We were sure to nurse first though and honestly, some nights he took less than the 4 ounces, so I was happy about that. I think ultimately though the formula stays in their tummies longer.
The reason I decided to try formula was because my parents weened my daughter off of night feedings at six months (we had to go on a destination wedding in VT) and they did it with formula. Being the grandparents, they were not about to rush downstairs at midnight or 2 Am or whenever to heat up the breastmilk I had left for them to use so they kept a few powdered bottles upstairs near the baby. I think she decided she did not like the taste and gave up on night feedings completely. Honestly, what happened those 5 days and 4 nights is still a mystery to me, but she seems no worse for the wear :-)
The decision is really up to you, but for us, with a third in the oven, I really needed to get the sleep so we went for the formula. The other nice thing is now Daddy can help wrap up the nighttime routine by passing off baby and the bottle to him. :-)
Good luck.
~C.